The two men -- a billionaire and a democratic socialist -- expressed interest in a televised encounter between them even though Republican and Democratic presidential candidates traditionally do not debate each other until the parties have selected their nominees.

"I'd love to debate Bernie, but they have to pay a lot of money for it," Trump told reporters in North Dakota, after he secured enough delegates to clinch the Republican presidential nomination.

When asked how much, Trump responded, "If we can raise for maybe women's health issues or something, if we can raise $10 or $15 million for charity."

Trump spokeswoman Hope Hicks said in an email that there were no formal plans yet for such an event. But Sanders campaign manager Jeff Weaver told CNN that there had been "a few discussions" between the campaigns about the details.

"We hope that he will not chicken out," Weaver said. "We hope Donald Trump has the courage to get on stage now that he said he would."

Sanders, a U.S. senator from Vermont, is running far behind Clinton in the race for the Democratic nomination for the Nov. 8 presidential election.

But a nationally televised debate with the presumptive Republican nominee would be a big boost to his chances in the California primary on June 7, when Clinton is likely to win the nomination.

In a September op-ed for CNN, then-Republican presidential candidate Jindal described Trump as "a shallow, unserious, substance-free, narcissistic egomaniac."

"We can decide to win, or we can be the biggest fools in history and put our faith not in our principles, but in an egomaniac who has no principles," Jindal wrote.

But following Trump's victory in the Republican presidential primary, Jindal offered a very tepid endorsement of the real-estate magnate.

"I think electing Donald Trump would be the second-worst thing we could do this November, better only than electing Hillary Clinton to serve as the third term for the Obama administration’s radical policies," Jindal wrote in The Wall Street Journal.

REUTERS/Brian C. Frank

Former Texas Gov. Rick Perry

During his short-lived 2016 presidential bid, Perry called Trump a "cancer on conservatism" and criticized his inflammatory rhetoric about Mexican immigrants.

"Demeaning people of Hispanic heritage is not just ignorant. It betrays the example of Christ," Perry said in his September concession speech. "We can enforce our laws and our borders, and we can love all who live within our borders, without betraying our values."

But after Sen. Ted Cruz dropped out of the race last week, Perry quickly endorsed the presumptive nominee.

"He is not a perfect man," Perry told CNN. "But what I do believe is that he loves this country and he will surround himself with capable, experienced people and he will listen to them."

REUTERS/Aaron Josefczyk

Sen. Rand Paul (Kentucky)

Last month, Paul said he would support Trump in a likely matchup between Democratic presidential frontrunner Hillary Clinton.

But in the lead-up to the Iowa caucuses, the former presidential candidate wasn't as fond of Trump, comparing him to infamous Nazi propagandist Joseph Goebbels.

"Donald Trump is a delusional narcissist and an orange-faced windbag," Paul said on Comedy Central.

He added: "A speck of dirt is more qualified to be president."

REUTERS/Scott Morgan

Sen. Marco Rubio (Florida)

Toward the end of his 2016 presidential bid, Rubio unleashed a flurry of rhetorical attacks on Trump.

Among other things, the Florida senator criticized Trump's hypocritical immigration policy prescriptions, joked about Trump urinating in his pants at a GOP debate, and questioned whether voters should hand "the nuclear codes of the United States to an erratic individual."

But last month, Rubio began to shift tone. He said he would support any Republican candidate, including Trump, though he ruled out any interest in being Trump's vice president.

REUTERS/Carlo Allegri

South Carolina Gov. Nikki Haley

Haley confirmed last week that she would "respect the will of the people" and would support Trump's candidacy.

Haley's tune was less favorable in February, when she hit the primary campaign trail in her home state for Sen. Marco Rubio, prompting Trump's ire.

Christie became the first major former presidential candidate to endorse Trump. But just a few months earlier, he was warning voters about Trump's preparedness for the office.

"We do not need reality TV in the Oval Office right now," Christie said in December. "President of the United States is not a place for an entertainer."

REUTERS/Chris Keane

Wisconsin Gov. Scott Walker

When Walker dropped out of the presidential race after just three months, the governor called on many of his Republican presidential rivals to do the same in order to consolidate support around a conservative candidate.

The governor took a thinly veiled shot at Trump, criticizing the real-estate mogul's brash rhetorical style.

"It has drifted into personal attacks. In the end, I believe that the voters want to be for something and not against someone," Walker said in his concession speech. "Instead of talking about how bad things are, we want to hear how we can make them better for everyone."

Yet late last month, Walker signaled he'd support the GOP nominee against Clinton — though he refused to say Trump's name.

Patrick T. Fallon/Bloomberg via Getty Images

Sen. Tim Scott (South Carolina)

Scott, a former Rubio endorser, said last week that he would support the Republican presidential nominee.

Though Scott was not a particularly vocal critic of the real-estate magnate, he did condemn Trump's initial refusal to denounce an endorsement from the former leader of the Ku Klux Klan.

"Any candidate who cannot immediately condemn a hate group like the KKK does not represent the Republican Party, and will not unite it," Scott wrote in a statement. "If Donald Trump can’t take a stand against the KKK, we cannot trust him to stand up for America against Putin, Iran, or ISIS."

Andrew Harrer/Bloomberg via Getty Images

Sen. Thom Tillis (North Carolina)

In an interview on Fox Business last year, Tillis, who recently said he would endorse Trump, characterized the former reality-television star's Republican-debate performance as "more entertainment" than policy. He also criticized the presumptive nominee's rhetoric for inciting violence at campaign rallies.

"He has some responsibility for it," Tillis said of the violence at Trump's rallies.

Drew Angerer/Getty Images

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The idea was hatched during an appearance by Trump on ABC's "Jimmy Kimmel Live" late on Wednesday. Kimmel said he asked Trump about the debate at the suggestion of Sanders, who is scheduled to appear on the show Thursday night.

The Clinton campaign did not immediately respond to a request for comment on a possible Trump-Sanders debate.

"Smart and bold move by Sanders," Democratic strategist Brad Bannon said. "Sanders will also have a chance mano on mano with Trump to prove that he would be a better candidate against Trump in November. The Clinton people are furious but Bernie wins points for being so aggressive."

Sanders has said he will do everything he can to ensure that Trump does not win the White House.

Clinton has tried to woo Sanders supporters as she turns her attention on the November election. But some worry that his supporters - who are largely young, working-class and disillusioned with the Democratic Party establishment - will turn instead to political neophyte Trump, who has championed a populist agenda.

The debate would give Trump a national forum to criticize Clinton and try to win over Sanders supporters ahead of an expected Trump-Clinton general election match-up, Democratic strategist Chris Kofinis said.

"I think Sanders should think long and hard about giving Trump a forum," he said. "It crosses a line, but apparently in this election there is no line,"

Dale Ranney, 62, a Trump volunteer who has been to 21 of his rallies, said she would be delighted to see Trump and Sanders debate.

"I think it's a great idea, any time you can get more information to the people, absolutely," Ranney said. "Having Trump debate a socialist? Absolutely. Go for it."